Multiplex mri image reconstruction

ABSTRACT

In Multiplex MRI image reconstruction, a hardware processor acquires sub-sampled Multiplex MRI data and reconstructs parametric images from the sub-sampled Multiplex MRI data. A machine learning model or deep learning model uses the subsampled Multiplex MRI data as the input and parametric maps calculated from the fully sampled data, or reconstructed fully sample data, as the ground truth. The model learns to reconstruct the parametric maps directly from the subsampled Multiplex MRI data.

FIELD

The aspects of the disclosed embodiments relate generally to MRI imagereconstruction, and more particularly to multiplex MRI imagereconstruction.

BACKGROUND

The multi-flip-angle (FA) and multi-echo gradient recalled echo (GRE)method (referred to herein as “Multiplex MRI”) provides the ability tosimultaneously acquire multiple contrast images with a single scan. OneMultiplex MRI scan offers multiple sets of images, including but notlimited to: composited PDW/T1W/T2*W, aT1W, SWI, MRA, Blt map, T1 map,T2*/R2* maps, PD map, and QSM. One example of such a method is describedin U.S. Patent Publication No. 2021/0011104 A1, entitled SYSTEMS ANDMETHODS FOR MAGNETIC RESONANCE IMAGING filed on Jul. 12, 2019 andpublished on Jan. 14, 2021, the disclosure of which is incorporated byreference herein in its entirety.

Current workflows to reconstruct the Multiplex MRI images generallyinclude two steps. The first step is to reconstruct each echo image fromk-spaces, where each echo image corresponds to one configuration of echoand FA settings. The reconstructed echo images have different contrastsand are aligned. In the second step, the parametric images or maps areprocessed based on the reconstructed echo images.

Multiplex MRI acquisition results in a relatively long scan time. Tospeed up the acquisition process, only the subsampled data can beacquired. However, reconstructing the echo images as well as theparametric maps from the subsampled Multiplex MRI data can be quitechallenging.

Accordingly, it would be desirable to provide methods and apparatus thataddress at least some of the problems described above.

SUMMARY

The aspects of the disclosed embodiments are directed to an apparatusand method for Multiplex MRI image reconstruction. This and otheradvantages of the disclosed embodiments are provided substantially asshown in, and/or described in connection with, at least one of thefigures, as set forth in the independent claims. Further advantageousmodifications can be found in the dependent claims.

According to a first aspect, the disclosed embodiments provide anapparatus for Multiplex MRI image reconstruction. In one embodiment, theapparatus includes a hardware processor that is configured to acquiresub-sampled Multiplex MRI data and reconstruct parametric images fromthe sub-sampled Multiplex MRI data. The aspects of the disclosedembodiments enable the reconstruction of the parametric maps or imagesdirectly from the sub-sampled raw Multiplex MRI data.

In a possible implementation form, a machine learning model is trainedto reconstruct the parametric maps directly from the sub-sampled data.The machine learning model is trained using sub-sampled Multiplex MRIdata and parametric maps calculated from fully sampled data. During thetraining, the machine learning model takes the sub-sampled Multiplex MRIdata as an input and generates a prediction as an output. The predictionis then compared to the parametric maps as the ground truth to train themodel. According to the aspects of the disclosed embodiments, themachine learning model, which can be a deep learning model, learns toreconstruct the parametric maps directly from the sub-sampled MultiplexMRI data without reconstructing the echo images.

In a possible implementation form, during testing, the hardwareprocessor is configured to reconstruct echo images from the sub-sampledMultiplex MRI data. Multiple echo images can be reconstructed togetherfrom the sub-sampled Multiplex MRI data so that the correlation betweendifferent echo images can be explored and utilized for better imagereconstruction quality.

In a possible implementation form, during testing, the hardwareprocessor is configured to generate the parametric maps from the echoimages reconstructed from the sub-sampled Multiplex MRI data. Stackingmultiple input images can be applied to both direct reconstruction andindirect reconstruction workflows.

In a possible implementation form, during testing, the hardwareprocessor is configured to stack multiple echo images and input thestacked echo images into the machine learning model. Stacking the framesis to provide more information for echo image reconstruction. Becausedifferent echo images have different contrasts and provide differentinformation about the underlying anatomy. By stacking the echo images,the model can then take more information as input.

In a possible implementation form, different sampling masks are used inacquisition of the Multiplex MRI image data. When the raw Multiplex MRIimage data is acquired by subsampling, some of the original informationis lost due to the subsampling. By using different sampling masks, theacquired information can be complementary. The designs of the differentmasks can be such that they subsample different regions. Duringreconstruction, the complementary information can be combined to recoverthe missing information.

In a possible implementation form, the sampling masks are configured toacquire information that is unique to a particular echo image.Information in different echo images can be redundant. For example, theoverall anatomical structures may be the same or similar acrossdifferent echo images. The sampling mask used in certain echo images canacquire different high frequency regions from the sampling mask used inother echo images. The high frequency information is helpful to recoverthe details in the image, which is important in the clinicalapplication.

In a possible implementation form, the subsampled data is divided intotwo or more parts in a readout (RO) direction. Instead of reconstructingthe full images at once, the images can be divided into several partsand each part can be reconstructed separately, which can then becombined into the final full images. This is useful in reducing memoryconsumption.

In a possible implementation form, a coil compression method is used.The coil compression is configured to reduce the number of coils. Usingfewer compression coils to acquire the raw image data for reconstructionreduces the amount of data. This promotes speed and efficiency of theprocess.

In a possible implementation form, the machine learning model is aconvolutional neural network (CNN) based deep learning model. Themethods used for reconstruction can be compressed sensing (CS) basedmethods or deep learning based methods.

According to a second aspect, the disclosed embodiments provide a methodfor Multiplex MRI image reconstruction. In one embodiment, the methodincludes acquiring sub-sampled Multiplex MRI data and reconstructingparametric images from the sub-sampled Multiplex MRI data. The aspectsof the disclosed embodiments enable the reconstruction of the parametricmaps or images directly from the sub-sampled raw Multiplex MRI datawithout reconstructing the echo images for Multiplex MRI.

According to a third aspect, the disclosed embodiments are directed to asystem for Multiplex MRI image reconstruction. In one embodiment, thesystem includes a server that includes a processor configured to acquiresub-sampled Multiplex MRI data and reconstruct parametric images fromthe sub-sampled Multiplex MRI data. The aspects of the disclosedembodiments reconstruct the parametric images directly from thesub-sampled raw data without reconstructing the echo images forMultiplex MRI. The aspects of the disclosed embodiments enable thereconstruction of the parametric maps or images directly from thesub-sampled raw Multiplex MRI data without reconstructing the echoimages for Multiplex MRI.

According to a fourth aspect the disclosed embodiments are directed to acomputer program product embodied on a non-transitory computer-readablemedium having machine readable instructions stored thereon, which, whenexecuted by a computer cause the computer to execute the processesassociated with aspects of one or more of the possible implementationforms described herein.

The aspects of the disclosed embodiments enable an accurate,computational power efficient, and memory efficient framework forunder-sampled or sub-sampled Multiplex MRI data reconstruction. Goodperformance in image quality as well as reconstruction time is realized.

These and other aspects, implementation forms, and advantages of theexemplary embodiments will become apparent from the embodimentsdescribed herein considered in conjunction with the accompanyingdrawings. It is to be understood, however, that the description anddrawings are designed solely for purposes of illustration and not as adefinition of the limits of the disclosed invention, for which referenceshould be made to the appended claims. Additional aspects and advantagesof the invention will be set forth in the description that follows, andin part will be obvious from the description, or may be learned bypractice of the invention. Moreover, the aspects and advantages of theinvention may be realized and obtained by means of the instrumentalitiesand combinations particularly pointed out in the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

In the following detailed portion of the present disclosure, theinvention will be explained in more detail with reference to the exampleembodiments shown in the drawings, in which:

FIG. 1 is a block diagram of an exemplary system for multiplex MRI imagereconstruction, in accordance with the aspects of the disclosedembodiments.

FIG. 2 is a block diagram of exemplary components of an apparatusincorporating aspects of the disclosed embodiments.

FIGS. 3 and 4 are illustrations of exemplary workflows incorporatingaspects of the disclosed embodiments.

FIG. 5 is a block diagram of an exemplary architecture for a machinelearning model incorporating aspects of the disclosed embodiments.

In the accompanying drawings, an underlined number is employed torepresent an item over which the underlined number is positioned or anitem to which the underlined number is adjacent. A non-underlined numberrelates to an item identified by a line linking the non-underlinednumber to the item. When a number is non-underlined and accompanied byan associated arrow, the non-underlined number is used to identify ageneral item at which the arrow is pointing.

DETAILED DESCRIPTION OF THE DISCLOSED EMBODIMENTS

The following detailed description illustrates exemplary aspects of thedisclosed embodiments and ways in which they can be implemented.Although some modes of carrying out the aspects of the disclosedembodiments have been disclosed, those skilled in the art wouldrecognize that other embodiments for carrying out or practising theaspects of the disclosed embodiments are also possible.

FIG. 1 is a block diagram of an exemplary system or apparatus 100 forMultiplex MRI image reconstruction in accordance with the aspects of thedisclosed embodiments. The aspects of the disclosed embodiments aredirected to reconstructing Multiplex MRI images. In one embodiment, acomputing device 102 of the system 100 includes a processor 104 that isconfigured to acquire sub-sampled Multiplex MRI data and reconstructparametric images directly from the sub-sampled Multiplex MRI data. Thiscan occur without reconstructing the echo images.

Multi-flip-angle (FA) and multi-echo GRE (hereinafter “Multiplex MRI”),can simultaneously acquire multiple contrast images with just one singlescan. With the single scan, Multiplex MRI can provide over 16 types ofimage contrasts and 9 types of parametric mappings. One Multiplex MRIscan often includes a combination of several echoes and differentflip-angles and each combination leads to one echo image. With differentecho and FA configure settings, a single scan can generate multiple(e.g., 7×2=14) echo data. Each echo image has different contrastinformation and the parametric maps, such as proton density weighted(PDW), T1 weighted (T1W), T2*, quantitative susceptibility mapping(QSM), can then be calculated based on the echo images.

With reference to FIG. 1 , the system 100 includes an apparatus 102,such as a computing device or server. Although a server is describedherein, and shown merely for illustration, the aspects of the disclosedembodiments are not so limited. In alternate embodiments, the apparatus102 can comprise any suitable computing or processing apparatus, otherthan including a server.

In one embodiment, the apparatus 102 includes a processor 104, a neuralnetwork or machine learning model 106 and a memory 106. The processor104, model 106 and memory 108 can be embodied in a single device or cancomprise multiple devices communicatively coupled together.

There is further shown a communication network 110 and imaging system120 or apparatus. The communication network 110 generally includes amedium through which the imaging system 120 and the apparatus 102 cancommunicate with each other. The imaging system 120, which can compriseany suitable MRI imaging stem, is configured to provide the MultiplexMRI data to the apparatus 102.

Although communication network 110 is shown communicatively coupling theimaging system 120 to the apparatus 102, the aspects of the disclosedembodiments are not so limited. In alternate embodiments the apparatus102 can be connected or coupled to the imaging system 120 in anysuitable manner. Additionally, the apparatus 102 can be configured toreceive, acquire or generate Multiplex MRI data, as is generallydescribed herein, from any suitable source in any suitable manner.

The aspects of the disclosed embodiments are directed to reconstructingparametric images or maps directly from the subsampled Multiplex MRIdata without reconstructing the echo images for Multiplex MRI. In oneembodiment, the workflow can be achieved by training the machinelearning model 106, also referred to as a deep learning model, usingsubsampled Multiplex MRI data as the input. During the training phase,parametric maps are calculated from the fully sampled Multiplex MRIdata, or reconstructed fully sampled Multiplex MRI data, as the groundtruth. The model 106 learns to reconstruct the parametric maps directlyfrom the subsampled Multiplex MRI data by comparing the prediction ofthe model 106 during the training phase to the ground truth and updatingthe model weights. Once the model 106 is fully trained, the model 106can be implemented in testing. During the testing phase, fully sampledMultiplex MRI data is not available.

FIG. 3 illustrates one embodiment of a workflow 300 incorporatingaspects of the disclosed embodiments. In this example, the parametricmaps 308 are reconstructed directly from the sub-sampled Multiplex MRIdata 302. The Multiplex MRI data is generally acquired through agradient echo (GRE) based method for single-scan 3D multi-parametricMRI. The single scan can offer multiple sets of images, including butnot limited to B1t and T1 maps, qualitative images of T1W, protondensity weighted (PDW), T2* augmented T1W (aT1W), susceptibilityweighted imaging (SWI), and optionally MR angiography (MRA), as well asparametric maps of T2* (R2*), PD, and quantitative susceptibilitymapping (QSM). Reference is made to U.S. Patent Publication No.2021/0011104 A1, Ser. No. 16/510,285, the disclosure of which isincorporated herein by reference in its entirety.

As illustrated in the example of FIG. 3 , the sub-sampled Multiplex MRIdata 302 is acquired. In one embodiment, the sub-sampled Multiplex MRIdata 402 indicates or is representative of the sub-sampled k-space.During an MRI scan, the Multiplex MRI data obtained is k-space data. Toaccelerate the MRI scan, often only subset of the k-space data isacquired by subsampling.

In the embodiment of FIG. 3 , the sub-sampled Multiplex MRI data 302includes a combination of different echo and flip angle (FA)configurations, where each combination leads to one echo image. Thenumber of echo and flip angle combinations shown in FIG. 3 is merelyexemplary. In alternate embodiments, there can be any suitable number ofecho and flip angle combinations.

In one embodiment, the sampling masks used in each echo acquisition,shown in FIG. 3 as Mask 1 to Mask N, can be different. In some cases,information in different echo images can be different. For example,overall anatomical structures may be the same or similar acrossdifferent echo images. One or more of the Mask 1 to Mask N can bedesigned to acquire more unique information to each echo image. Forexample, the mask used in certain echo images can acquire different highfrequency regions from the mask used in other echo images. The highfrequency information is helpful to recover the details in the image,which is important in the clinical application.

By using different sampling masks, the acquired information can becomplementary. For example, for certain echo images, Mask 1 can be used.For other echo images, Mask 2 or Mask N can be used. The design of Mask1 to Mask N is configured so that different regions of the data aresub-sampled. During reconstruction, complementary information iscombined to recover the missing information.

In one embodiment, a machine learning model or module 306 receives asinput 304, the sub-sampled Multiplex MRI data 302. The machine learningmodel 306 in this example is similar to the machine learning model 108of FIG. 1 . In this example, the machine learning model 306 isconfigured to reconstruct the parametric maps 308 from the sub-sampledMultiplex MRI data.

During training of the machine learning model 306, the machine learningmodel 306 receives the sub-sampled Multiplex MRI data 304 as the input304 and outputs a prediction. The fully sampled Multiplex MRI data 310is the ground truth. The prediction is compared to the ground truth andthe model weights are updated 312 during the training phase.

During testing, the model 306 takes the sub-sampled Multiplex MRI data304 as the input. The model 306 then generates or calculates theparametric maps 308.

In one embodiment, the input 304 can comprise the sub-sampled MultiplexMRI data with some pre-processing. This pre-processing can result in,for example, but is not limited to coil compressed data or read out (RO)cropped data.

For example, a coil compression method can be used to reduce the numberof coils such that fewer compressed coils are used for reconstruction.As another example, instead of reconstructing the full images at once,the images can be divided into several parts by readout direction andeach part can be reconstructed separately, which can then be combinedinto the final full images. These can be considered data pre-processingsteps.

In one embodiment, the machine learning model 306, similarly to theneural network 106 of FIG. 2 , comprises a deep learning network, suchas a convolutional neural network (CNN). In alternate embodiment, themachine learning model 306 can include any suitable machine learningmodel, other than include a CNN.

Referring to FIG. 4 , in one embodiment, the echo images are firstreconstructed. In this manner, multiple echo images can be reconstructedtogether such that the correlation between different echo images can beexplored and utilized for better image reconstruction quality and speed.

As shown in the exemplary workflow 400 of FIG. 4 , in this example, themachine learning model 406, similar to models 106 and 306 reconstructsthe echo images 408 from the sub-sampled Multiplex MRI data 402. Theparametric maps 410 are generated or calculated from the reconstructedecho images 410. The reconstructed echo images 408 are an intermediateresult of the workflow 400.

In one embodiment, multiple echo images can be reconstructed together.This can be implemented, for example, by stacking the multiple echoimages as an extra dimension in the input 404 and feeding the stack asthe input 404 into the machine learning model 406. By stacking the echoimages, the machine learning model 406 can take more information asinput.

In the example workflows of FIGS. 3 and 4 , the methods used forreconstruction can be CS based methods or deep learning based methods.For example, the models 306 and 406 can be a CNN based deep learningmodel.

FIG. 5 illustrates one embodiment of an exemplary network architecture500 for Multiplex data reconstruction. The architecture 500 can beimplemented in the model 306 and 406 of FIGS. 3 and 4 . In this example,the architecture 500, includes five convolutional blocks 502. Each block502 will include five Convolutional layers 504 and one data consistencylayer 506. The feature maps are forty-eight (48) for the first four (4)convolutional layers and two (2) for the last convolutional layer ineach block. The x, y inputs indicate sub-sampled image inputs andk-space inputs, respectively. The real and imaginary numbers of complexvalues are transformed into two channels and fed into the network.

The architecture 500 is merely exemplary. In alternate embodiments, anysuitable network architecture can be used to implement the models306/406 described herein.

Referring again to FIG. 1 , the apparatus 102 includes suitable logic,circuitry, interfaces and/or code that is configured to receive thesub-sampled Multiplex MRI data as is described herein. Examples of theapparatus 102 may include, but are not limited to, an applicationserver, a web server, a database server, a file server, a cloud server,or a combination thereof.

In one embodiment, the processor 104 includes suitable logic, circuitry,interfaces and/or code that is configured to carry out the processesgenerally described herein. The processor 104 is configured to respondto and process instructions that drive the apparatus 102. Examples ofthe processor 104 includes, but is not limited to, a microprocessor, amicrocontroller, a complex instruction set computing (CISC)microprocessor, a reduced instruction set (RISC) microprocessor, a verylong instruction word (VLIW) microprocessor, or any other type ofprocessing circuit. Optionally, the processor 104 may be one or moreindividual processors, processing devices and various elementsassociated with a processing device that may be shared by otherprocessing devices. Additionally, the one or more individual processors,processing devices and elements are arranged in various architecturesfor responding to and processing the instructions that drive theapparatus 102. In one embodiment, the processor 104 is a hardwareprocessor.

The memory 106 may comprise suitable logic, circuitry, interfaces,and/or code that may be configured to store instructions executable bythe processor 104. The memory 202 is further configured to store the MRIdata. The memory 106 may be further configured to store operatingsystems and associated applications of the apparatus 102 including theneural network 108. Examples of implementation of the memory 106 mayinclude, but are not limited to, Random Access Memory (RAM), Read OnlyMemory (ROM), Hard Disk Drive (HDD), Flash memory, and/or a SecureDigital (SD) card. A computer readable storage medium for providing anon-transient memory may include, but is not limited to, an electronicstorage device, a magnetic storage device, an optical storage device, anelectromagnetic storage device, a semiconductor storage device, or anysuitable combination of the foregoing.

The neural network 108 generally refers to an artificial neural network.In one embodiment, the neural network 108 is an unsupervised neuralnetwork that uses machine learning.

The communication network 110 may be a wired or wireless communicationnetwork. Examples of the communication network 110 may include, but arenot limited to, a Wireless Fidelity (Wi-Fi) network, a Local AreaNetwork (LAN), a wireless personal area network (WPAN), a Wireless LocalArea Network (WLAN), a wireless wide area network (WWAN), a cloudnetwork, a Long Term Evolution (LTE) network, a plain old telephoneservice (POTS), a Metropolitan Area Network (MAN), and/or the Internet.

In one embodiment, referring also to FIG. 2 , a user interface 112, suchas a display, can be used to present the results of the processinggenerally described herein. For example, in one embodiment, theparametric images can be presented on the user interface 112 forvisualization and use.

Referring again to FIG. 1 , in one aspect, the disclosed embodimentsinclude a training phase and an operational or testing phase. In thetraining phase, the neural network 106, which can comprise or includeone or more of the machine learning models 306 and 406 described herein,is trained, using sub-sampled Multiplex MRI data as the training data,to enable the neural network 106 to perform specific intended functionsin the operational phase. The processor 104 is configured to execute anunsupervised or a semi-supervised training of the neural network 106using the training data. In one embodiment, in the unsupervised trainingof the neural network 106, unlabeled training data is used for trainingof the neural network 106. In one embodiment, in the semi-supervisedtraining of the neural network 106, a comparatively small amount oflabeled training data and a large amount of unlabeled training data isused for training of the neural network 106.

Various embodiments and variants disclosed above, with respect to theaforementioned system 100, apply mutatis mutandis to the method. Themethod described herein is computationally efficient and does not causeprocessing burden on the processor 104.

Modifications to embodiments of the aspects of the disclosed embodimentsdescribed in the foregoing are possible without departing from the scopeof the aspects of the disclosed embodiments as defined by theaccompanying claims. Expressions such as “including”, “comprising”,“incorporating”, “have”, “is” used to describe and claim the aspects ofthe disclosed embodiments are intended to be construed in anon-exclusive manner, namely allowing for items, components or elementsnot explicitly described also to be present. Reference to the singularis also to be construed to relate to the plural.

Thus, while there have been shown, described and pointed out,fundamental novel features of the invention as applied to the exemplaryembodiments thereof, it will be understood that various omissions,substitutions and changes in the form and details of devices and methodsillustrated, and in their operation, may be made by those skilled in theart without departing from the spirit and scope of the presentlydisclosed invention. Further, it is expressly intended that allcombinations of those elements, which perform substantially the samefunction in substantially the same way to achieve the same results, arewithin the scope of the invention. Moreover, it should be recognizedthat structures and/or elements shown and/or described in connectionwith any disclosed form or embodiment of the invention may beincorporated in any other disclosed or described or suggested form orembodiment as a general matter of design choice. It is the intention,therefore, to be limited only as indicated by the scope of the claimsappended hereto.

What is claimed is:
 1. An apparatus for Multiplex MRI imagereconstruction, comprising: a hardware processor coupled to a memory,wherein the hardware processor is configured to: acquire sub-sampledMultiplex MRI data; and reconstruct parametric maps from the sub-sampledMultiplex MRI data.
 2. The apparatus according to claim 1, wherein thehardware processor is further configured to train a machine learningmodel to reconstruct the parametric maps from the acquired sub-sampledMultiplex MRI data using sub-sampled Multiplex MRI data as an input andparametric maps reconstructed from fully sampled Multiplex MRI data asthe ground truth.
 3. The apparatus according to claim 1, wherein thehardware processor is further configured to reconstruct echo images withthe acquired sub-sampled Multiplex MRI data prior to reconstructing theparametric maps.
 4. The apparatus according to claim 3, wherein theacquired sub-sampled Multiplex MRI data comprises echo images and thehardware processor is further configured to stack multiple ones of theecho images and input the stacked images into the machine learningmodel.
 5. The apparatus according to claim 1, wherein the hardwareprocessor is configured to acquire the sub-sampled Multiplex MRI datausing different sampling masks.
 6. The apparatus according to claim 1,wherein the hardware processor is further configured to divide theacquired sub-sampled Multiplex MRI data into two or more parts in areadout (RO) direction.
 7. A computer implemented method for multiplexMRI reconstruction, the method comprising using a hardware processor to:acquire sub-sampled Multiplex MRI data; and reconstruct parametric mapsfrom the sub-sampled Multiplex MRI data.
 8. The computer implementedmethod according to claim 7, the method further comprising training amachine learning model to reconstruct the parametric maps from theacquired sub-sampled Multiplex MRI data using sub-sampled Multiplex MRIdata as an input and parametric maps reconstructed from fully sampledMultiplex MRI data as the ground truth
 9. The computer implementedmethod according to claim 8, wherein the method further comprisesreconstructing echo images with the acquired sub-sampled Multiplex MRIdata prior to reconstructing the parametric maps.
 10. The computerimplemented method according to claim 9, wherein the acquiredsub-sampled Multiplex MRI data comprises echo images and the methodfurther comprises stacking multiple ones of the echo images andinputting the stacked images into the machine learning model.
 11. Thecomputer implemented method according to claim 9, wherein the methodfurther comprises applying different sampling masks to different echoimages of the sub-sampled Multiplex MRI data.
 12. The computerimplemented method according to claim 8, wherein the method furthercomprises dividing the acquired sub-sampled Multiplex MRI data into twoor more parts in a readout (RO) direction; reconstructing the two ormore parts separately, and combining the reconstructed two or more partsinto a final full image.
 13. A computer program product comprising anon-transitory computer-readable medium having machine readableinstruction stored thereon, which when executed by a computingapparatus, are configured to cause the computing apparatus to executethe method according to claim 7.